In the last decade, there have been an increasing convergence of interest and methods between theoretical physics and fields as diverse as probability, machine learning, optimization and compressed sensing. In particular, many theoretical and applied works in statistical physics and computer science have relied on the use of message passing algorithms and their connection to statistical physics of spin glasses. The aim of this book, especially adapted to PhD students, post-docs, and young researchers, is to present the background necessary for entering this fast developing field.

This book gathers the lecture notes of courses given at the 2011 summer school in theoretical physics in Les Houches, France, Session XCVI. What is a quantum machine? Can we say that lasers and transistors are quantum machines? After all, physicists advertise these devices as the two main spin-offs of the understanding of quantum mechanical phenomena. However, while quantum mechanics must be used to predict the wavelength of a laser and the operation voltage of a transistor, it does not intervene at the level of the signals processed by these systems. Signals involve macroscopic collective variables like voltages and currents in a circuit or the amplitude of the oscillating electric field in an electromagnetic cavity resonator. In a true quantum machine, the signal collective variables, which both inform the outside on the state of the machine and receive controlling instructions, must themselves be treated as quantum operators, just as the position of the electron in a hydrogen atom. Quantum superconducting circuits, quantum dots, and quantum nanomechanical resonators satisfy the definition of quantum machines. These mesoscopic systems exhibit a few collective dynamical variables, whose fluctuations are well in the quantum regime and whose measurement is essentially limited in precision by the Heisenberg uncertainty principle. Other engineered quantum systems based on natural, rather than artificial degrees of freedom can also qualify as quantum machines: trapped ions, single Rydberg atoms in superconducting cavities, and lattices of ultracold atoms. This book provides the basic knowledge needed to understand and investigate the physics of these novel systems.

This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. Written in a pedagogical style, this volume illustrates how the field of quantum gases has flourished at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics and quantum information. The physics of correlated atoms in optical lattices is covered from both theoretical and experimental perspectives, including the Bose and Fermi Hubbard models, and the description of the Mott transition. Few-body physics with cold atoms has made spectacular progress and exact solutions for 3-body and 4-body problems have been obtained. The remarkable collisional stability of weakly bound molecules is at the core of the studies of molecular BEC regimes in Fermi gases. Entanglement in quantum many-body systems is introduced and is a key issue for quantum information processing. Rapidly rotating quantum gases and optically induced gauge fields establish a remarkable connection with the fractional quantum Hall effect for electrons in semiconductors. Dipolar quantum gases with long range and anisotropic interaction lead to new quantum degenerate regimes in atoms with large magnetic moments, or electrically aligned polar molecules. Experiments with ultracold fermions show how quantum gases serve as ''quantum simulators'' of complex condensed matter systems through measurements of the equation of state. Similarly, the recent observation of Anderson localization of matter waves in a disordered optical potential makes a fruitful link with the behaviour of electrons in disordered systems.

This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales." Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).

Over the last decade new experimental tools and theoretical concepts are providing new insights into collective nonequilibrium behavior of quantum systems. The exquisite control provided by laser trapping and cooling techniques allows us to observe the behavior of condensed bose and degenerate Fermi gases under nonequilibrium drive or after `quenches' in which a Hamiltonian parameter is suddenly or slowly changed. On the solid state front, high intensity short-time pulses and fast (femtosecond) probes allow solids to be put into highly excited states and probed before relaxation and dissipation occur. Experimental developments are matched by progress in theoretical techniques ranging from exact solutions of strongly interacting nonequilibrium models to new approaches to nonequilibrium numerics. The summer school `Strongly interacting quantum systems out of equilibrium' held at the Les Houches School of Physics as its XCIX session was designed to summarize this progress, lay out the open questions and define directions for future work. This books collects the lecture notes of the main courses given in this summer school.

This book gathers the lecture notes of courses given at Session CVII of the summer school in physics, entitled "Current Trends in Atomic Physics" and held in July, 2016 in Les Houches, France. Atomic physics provides a paradigm for exploring few-body quantum systems with unparalleled control. In recent years, this ability has been applied in diverse areas including condensed matter physics, high energy physics, chemistry and ultra-fast phenomena as well as foundational aspects of quantum physics. This book addresses these topics by presenting developments and current trends via a series of tutorials and lectures presented by international leading investigators.

Many of the distinctive and useful phenomena of soft matter come from its interaction with interfaces. Examples are the peeling of a strip of adhesive tape, the coating of a surface, the curling of a fiber via capillary forces, or the collapse of a porous sponge. These interfacial phenomena are distinct from the intrinsic behavior of a soft material like a gel or a microemulsion. Yet many forms of interfacial phenomena can be understood via common principles valid for many forms of soft matter. Our goal in organizing this school was to give students a grasp of these common principles and their many ramifications and possibilities. The Les Houches Summer School comprised over fifty 90-minute lectures over four weeks. Four four-lecture courses by Howard Stone, Michael Cates, David Nelson and L. Mahadevan served as an anchor for the program. A number of shorter courses and seminars rounded out the school. This volume collects the lecture notes of the school.

The book gathers lecture notes of courses given at the 2014 summer school on integrated biology in Les Houches, France, Session CII. It addresses an emerging field ranging from molecules to cells and to organisms. Through examples it presents a new way of thinking using a combination of interdisciplinary and cutting-edge methods, bridging physics and biology beyond current biophysics. Important novel developments are expected in the coming years that may well introduce paradigm shifts in biological science. The school had the ambition to prepare participants to become major actors in these breakthroughs. The power of integrated approaches is illustrated through two cases: interactions between viruses and host cells, and flower development. The role of forces in biology, as well as their mathematical modeling, is illustrated in both processes: how they allow flower organs to emerge or how they control membrane fusion during virus budding. The book also underlines the importance of conformational changes and dynamics of proteins particularly during membrane processes. It explains how membrane proteins can be handled and studied by molecular simulations. Finally, the book also contains concepts in cell biology, in thermodynamics and several novel approaches such as in-cell NMR. Altogether, the chapters show how examining a biological system from different viewpoints based on multidisciplinary aspects often leads to enriching controversial arguments.

This book gathers the lecture notes of the 100th Les Houches Summer School, which was held in July 2013. These lectures represent a comprehensive pedagogical survey of the frontier of theoretical and observational cosmology just after the release of the first cosmological results of the Planck mission. The Cosmic Microwave Background is discussed as a possible window on the still unknown laws of physics at very high energy and as a backlight for studying the late-time Universe. Other lectures highlight connections of fundamental physics with other areas of cosmology and astrophysics, the successes and fundamental puzzles of the inflationary paradigm of cosmic beginning, the themes of dark energy and dark matter, and the theoretical developments and observational probes that will shed light on these cosmic conundrums in the years to come.